Supercomputers overturn 50-year-old conjecture of fluid physics

Researchers
from the Indian Institute of Technology (IIT) Kanpur have found a way out of a long-unsolved
problem in fluid mechanics with new studies1, 2 that characterise
‘buoyancy-driven flows’ more accurately, something that could overturn an
age-old conjecture in the physics of fluids. New insights into fluid motion
could improve marine and air travel and help create better weather prediction
models, and even better air-conditioning for households.

Using
large-scale numerical simulations on some of the best supercomputers of the
world, Mahendra Verma and colleagues at IIT Kanpur ran a home-grown numerical
code – TARANG – to create detailed simulations for buoyancy-driven flows. They
observed that the buoyancy driven turbulent flow is better characterised by a
model, first proposed by the Russian scientist Andrey Kolmogorov, instead of
the model proposed by R. Bolgiano and Alexander Obukhov, as was previously believed.

Fluid
motion is at the heart of our understanding of everything that involves motions
of fluids – from flowing rivers to blowing winds or even a steaming cup of hot coffee.
Turbulence occurs when there are chaotic changes in the pressure and flow
velocity of a moving fluid. Turbulent motion can be seen on the surface as also
interiors of the earth, planets, sun and stars. Buoyancy, the force that fluids
exert on subjects immersed in them, also drives and influences flows. Flows
influenced by buoyancy are called buoyancy driven flows.

“The
atmosphere of earth has shear (difference in flow speeds at different
locations) driven turbulence as well as buoyancy driven turbulence”, explains
Jayawant Arakeri from the mechanical engineering department of Indian Institute
of Science (IISc), Bengaluru.

The ‘unsolved’ problem

Is it
possible to describe precisely the behaviour of a fluid undergoing turbulent
flow, particularly its internal structure?

Russian
mathematician Andrey Kolmogorov had proposed the first statistical model for
hydrodynamic turbulence. The model suggests that energy cascades through the
liquid from large scale to small scale at a constant rate. It does not seem to spell
out the flow well as the energy transfer appears to reduce at smaller scales.

There
are multiple types of buoyancy driven flows, and each shows a different
behaviour3.

Verma
and colleagues worked on two of them. In one case, a heavier, colder fluid was
at the bottom of a container and a lighter, hotter fluid on top with no
vertical movement. Such systems are called ‘stably stratified’ and their
density and temperature change uniformly from bottom to top. The other system has
the lighter, hotter fluid at the bottom and the heavier, colder fluid on top –
the Rayleigh-Bènard convection.

The
IIT team carried out high resolution numerical simulations for both, the stably
stratified systems and Rayleigh-Bènard convection. They observed that stably
stratified systems follow the Bolgiano-Obukov model but contrary to the earlier
belief, Rayleigh-Bènard Convection followed the Kolmogorov model.

“This
is a fundamental result. It is important to note that due to the detailed
simulations carried out, all scales were resolved,” Arakeri says.

Verma’s
team implemented their code on the supercomputers at King Abdullah University,
Saudi Arabia’s Shaheen II and the supercomputer at Indian Institute of Science
(IISc), Bengaluru. It was essential to analyse the flow equations for as small
a volume as possible. The computation power required for the detailed
simulation was enormous. Certain aspects of energy transfer in turbulent fluids
could be established only because of the detailed, fine resolution
computations, Verma says.

This
analysis, he says, opens the door for future work on energy transfers in
various forms of fluid flows.